The factors of 48 are [1, 2, 3, 4, 6, 8, 12, 16, 24, 48] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 5 factors [1, 2, 4, 8, 16] making 16 the greatest factor 48 and 64 have in common.

There are 3 5-passenger taxis available so that's 3 x 5 = 15 total seats. There are 18 people needing transportation leaving 18 - 15 = 3 who will have to find other transportation.

To fill a 12 gallon tank exactly halfway you'll need 6 gallons of fuel. Each fuel can holds 2 gallons so:

cans = \( \frac{6 \text{ gallons}}{2 \text{ gallons}} \) = 3

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{5 x 3}{2 x 3} \) - \( \frac{7 x 1}{6 x 1} \)

\( \frac{15}{6} \) - \( \frac{7}{6} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{15 - 7}{6} \) = \( \frac{8}{6} \) = 1\(\frac{1}{3}\)

To subtract these radicals together their radicands must be the same:

8\( \sqrt{12} \) - 2\( \sqrt{3} \)
8\( \sqrt{4 \times 3} \) - 2\( \sqrt{3} \)
8\( \sqrt{2^2 \times 3} \) - 2\( \sqrt{3} \)
(8)(2)\( \sqrt{3} \) - 2\( \sqrt{3} \)
16\( \sqrt{3} \) - 2\( \sqrt{3} \)

Now that the radicands are identical, you can subtract them: